Details

analyze622.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 29 to 21 computations (27.6% saved)

sample77.0ms (0.8%)

Algorithm

1×

intervals

Results

47.0ms	256×	body	128	valid
6.0ms	35×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify264.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4968	9
1	4968	9

prune11.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.3b

Counts

2 → 2

Compiler

Compiled 40 to 32 computations (20% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac_binary64_84`
10×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139`
4×	`associate-/r*_binary64_22` `log-pow_binary64_167`
3×	`add-cbrt-cube_binary64_114` `associate-/l*_binary64_23` `add-exp-log_binary64_116`
1×	`add-log-exp_binary64_117` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77`

Counts

1 → 31

Calls

2 calls:

4.0ms	(/.f64 (atan2.f64 im re) (log.f64 base))
0.0ms	(/.f64 (atan2.f64 im re) (log.f64 base))

series267.0ms (2.8%)

Counts

1 → 9

Calls

1 calls:

267.0ms

(/.f64 (atan2.f64 im re) (log.f64 base))

Compiler

Compiled 126 to 126 computations (0% saved)

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4804	572
1	4804	572

prune90.0ms (1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	28	12	40
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	29	13	42

Error

0.0b

Counts

42 → 13

Compiler

Compiled 614 to 185 computations (69.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))
0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))
0.3b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_84`
60×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`associate-/r*_binary64_22` `pow1_binary64_139`
16×	`log-pow_binary64_167`
15×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114`
8×	`div-exp_binary64_129`
7×	`associate-/l*_binary64_23`
6×	`div-inv_binary64_75`
4×	`cbrt-undiv_binary64_112`
2×	`add-log-exp_binary64_117` `frac-2neg_binary64_89` `1-exp_binary64_122` `rec-exp_binary64_128` `clear-num_binary64_77`
1×	`inv-pow_binary64_163` `pow-flip_binary64_152` `associate-/r/_binary64_24`

Counts

2 → 119

Calls

4 calls:

7.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
6.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
0.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
0.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

series548.0ms (5.8%)

Counts

2 → 18

Calls

2 calls:

302.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
246.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

Compiler

Compiled 288 to 288 computations (0% saved)

simplify113.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5084	2435

prune167.0ms (1.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	136	14	150

Error

0.0b

Counts

150 → 14

Compiler

Compiled 2112 to 586 computations (72.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
0.3b	(/.f64 1 (log.f64 base))
0.3b	(/.f64 1 (log.f64 base))
0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_100`
26×	`times-frac_binary64_84`
21×	`*-un-lft-identity_binary64_78`
20×	`add-cube-cbrt_binary64_113`
16×	`associate-r_binary64_18`
15×	`add-exp-log_binary64_116`
12×	`pow1_binary64_139`
9×	`add-cbrt-cube_binary64_114`
7×	`log-pow_binary64_167`
4×	`prod-exp_binary64_127` `div-exp_binary64_129` `associate-/r*_binary64_22`
3×	`associate-l_binary64_19` `associate-/l*_binary64_23` `unswap-sqr_binary64_46`
2×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `1-exp_binary64_122` `div-inv_binary64_75` `rec-exp_binary64_128`
1×	`-commutative_binary64_9` `inv-pow_binary64_163` `un-div-inv_binary64_76` `frac-2neg_binary64_89` `pow-flip_binary64_152` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77`

Counts

2 → 74

Calls

4 calls:

11.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
6.0ms	(/.f64 1 (log.f64 base))
0.0ms	(/.f64 1 (log.f64 base))
0.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))

series446.0ms (4.7%)

Counts

2 → 12

Calls

2 calls:

322.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
123.0ms	(/.f64 1 (log.f64 base))

Compiler

Compiled 188 to 188 computations (0% saved)

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5058	929

prune81.0ms (0.9%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	10	11
Picked	0	1	1
Done	0	2	2
Total	86	14	100

Error

0.0b

Counts

100 → 14

Compiler

Compiled 1143 to 465 computations (59.3% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.6b	(cbrt.f64 (log.f64 base))
0.3b	(/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base)))
0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
0.3b	(/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))))
0.6b	(cbrt.f64 (log.f64 base))
0.6b	(cbrt.f64 (log.f64 base))
0.6b	(cbrt.f64 (log.f64 base))
0.6b	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_109`
23×	`add-sqr-sqrt_binary64_100`
20×	`pow1_binary64_139`
17×	`*-un-lft-identity_binary64_78`
15×	`add-cube-cbrt_binary64_113`
9×	`swap-sqr_binary64_45` `pow1/3_binary64_160` `log-pow_binary64_167`
7×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `unswap-sqr_binary64_46`
2×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-plus_binary64_141`

Counts

4 → 81

Calls

8 calls:

9.0ms	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))
1.0ms	(cbrt.f64 (log.f64 base))
1.0ms	(cbrt.f64 (log.f64 base))
1.0ms	(cbrt.f64 (log.f64 base))
0.0ms	(/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))))

series873.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))
227.0ms	(cbrt.f64 (log.f64 base))
225.0ms	(cbrt.f64 (log.f64 base))
171.0ms	(cbrt.f64 (log.f64 base))

Compiler

Compiled 488 to 402 computations (17.6% saved)

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4995	799
1	4995	799

prune109.0ms (1.2%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	4	6	10
Picked	0	1	1
Done	0	3	3
Total	96	11	107

Error

0.0b

Counts

107 → 11

Compiler

Compiled 1802 to 541 computations (70% saved)

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	177	829
1	177	829

regimes334.0ms (3.5%)

Accuracy

Total 0.3b remaining (97.1%)

Threshold costs 0.3b (97.1%)

Compiler

Compiled 2094 to 1598 computations (23.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end0.0ms (0%)

sample5.0s (53.6%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
135.0ms	1000×	body	128	nan

Compiler

Compiled 1592 to 1203 computations (24.4% saved)

Pareto

0.3393808190248813

Details

analyze622.0ms (6.6%)

sample77.0ms (0.8%)

simplify264.0ms (2.8%)

prune11.0ms (0.1%)

localize12.0ms (0.1%)

rewrite7.0ms (0.1%)

series267.0ms (2.8%)

simplify81.0ms (0.9%)

prune90.0ms (1%)

localize12.0ms (0.1%)

rewrite24.0ms (0.3%)

series548.0ms (5.8%)

simplify113.0ms (1.2%)

prune167.0ms (1.8%)

localize8.0ms (0.1%)

rewrite26.0ms (0.3%)

series446.0ms (4.7%)

simplify78.0ms (0.8%)

prune81.0ms (0.9%)

localize15.0ms (0.2%)

rewrite21.0ms (0.2%)

series873.0ms (9.3%)

simplify57.0ms (0.6%)

prune109.0ms (1.2%)

simplify26.0ms (0.3%)

regimes334.0ms (3.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.0s (53.6%)

Profiling